Related papers: The Fundamental Theorem of Perfect Simulation
We consider the Subset Sum Ratio Problem ($SSR$), in which given a set of integers the goal is to find two subsets such that the ratio of their sums is as close to~1 as possible, and introduce a family of variations that capture additional…
Transition Path Theory (TPT) provides a rigorous framework to investigate the dynamics of rare thermally activated transitions. In this theory, a central role is played by the forward committor function q^+(x), which provides the ideal…
A novel long-lived distributed problem, called Team Formation (TF), is introduced together with a message- and time-efficient randomized algorithm. The problem is defined over the asynchronous model with a complete communication graph,…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
This paper explores the computational complexity of diffusion-based language modeling. We prove a dichotomy based on the quality of the score-matching network in a diffusion model. In one direction, a network that exactly computes the score…
Positive semidefinite programs are an important subclass of semidefinite programs in which all matrices involved in the specification of the problem are positive semidefinite and all scalars involved are non-negative. We present a parallel…
We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random…
A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…
The idea of iterative process optimization based on collected output measurements, or "real-time optimization" (RTO), has gained much prominence in recent decades, with many RTO algorithms being proposed, researched, and developed. While…
We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier's verdict is a function of the XOR of the two bits received. We show that, when the provers are allowed to…
A sliding window algorithm receives a stream of symbols and has to output at each time instant a certain value which only depends on the last $n$ symbols. If the algorithm is randomized, then at each time instant it produces an incorrect…
It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is…
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
The problem of model identification for linear systems is considered, using a finite set of sampled data affected by a bounded measurement noise, with unknown bound. The objective is to identify one-step-ahead models and their accuracy in…
While standard computational protocols for density functional theory (DFT) have universal applicability, differences exist in code implementations. Specific applications require manual parameter optimization, whereas high-throughput…
We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of…
We consider the problem of finding the set of architectural parameters for a chosen deep neural network which is optimal under three metrics: parameter size, inference speed, and error rate. In this paper we state the problem formally, and…
In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a Finite Transition…
Motivated by the Model-Based Design process for Cyber-Physical Systems, we consider issues in conformance testing of systems. Conformance is a quantitative notion of similarity between the output trajectories of systems, which considers…